I've been aware of this "rule" for at least a decade, probably more.
The main reason -- as has been noted already -- is a courtesy not to compete with dealers who purchased their tables. Dealers can accept cash for chips. Also, dealers can exchange cash for chips from anyone who walks up to their table (One time, Charlie "C.T" Rogers told me he liked his table up front because locals occasionally walked in to sell chips, and he was positioned to see them first!)

Another reality is the South Point contract and the tax statements that all dealers must complete. Like it or not, every dealer who sells must file a sales tax statement at the end of the show. Any "private" sales that are untaxed could potentially expose the club (as holder of the contract with South Point) to consequences.

While a single, member-to-member discrete exchange probably would never get noticed, I wouldn't want this to get out of control. There may be technical differences in a private-club convention with sales vs. a totally-open-to-the-public event with sales. That's why I fully support Archie's / the club's requirement that all entrants must be identified, even on the free-entry Saturday.

I'm not a tax expert, but Jim P. could probably advise us, if necessary.